📏 Units

Alpaca4d works in one fixed set of units: metres, kilonewtons, seconds and radians, with masses and densities given in kilograms. The inputs and the result components use them, with the few exceptions listed below, and there is no setting to change them. Only Model View lets you choose the units it displays in.

The base units

Quantity	Unit
Length, coordinates, section dimensions, the Assemble Tolerance	m
Force	kN
Mass	kg
Time	s
Angle, rotation	rad

Everything else follows from them:

Quantity	Unit
Moment	kN·m
Line load, shell membrane force and transverse shear	kN/m
Pressure, stress, E and G	kN/m²
Shell bending moment	kN·m/m
Density	kg/m³
Area, second moment of area	m², m⁴
Spring stiffness	kN/m along, kN·m/rad about
Curvature	rad/m
Velocity, acceleration	m/s, m/s²
Period, frequency	s, Hz

Strains, Poisson's ratio and utilisations have no unit. The hinge lengths of Beam With Hinges are fractions of the element length, not lengths.

The exceptions

• Beam Stresses are in MPa (N/mm²), the unit design strengths are given in. Shell and brick stresses stay in kN/m². One MPa is 1000 kN/m².
• The Material Database stores E and G in MPa, and multiplies them by 1000 into kN/m² when it makes the material.
• Model View starts displacements in mm and stresses in MPa (see Units in Model View).

The Rhino document is read as metres

Alpaca4d never scales geometry. A coordinate goes into the OpenSees model as it stands and is read as metres, and so is the Tolerance. A model drawn in millimetres would come out a thousand times too big, so Assemble warns when the Rhino document is in any unit other than metres. Set the document to metres before you build the model.

What OpenSees assumes

OpenSees has no unit system. It takes every number as it is given, and the answer is right only when all of them are in units that fit together. Alpaca4d writes the deck in kN, m and s, and the mass unit that goes with them is the tonne (kN·s²/m), not the kilogram. So every mass and density you give in kg is divided by 1000 as the deck is written: element densities and Mass Point masses alike, so the two are on the same footing. Self-weight is worked out by Alpaca4d with g = 9.81 m/s².

Note

A ground-motion record in g is not converted for you. Multiply it by 9.81, in the file or on the Factor of its Load Pattern, so that it is in m/s².

A deck you write or edit by hand for Custom Code or Deserialise has to keep to the same units, since OpenSees cannot tell.

Units in Model View

Each result in Model View has a Unit menu of its own, which starts on the unit in bold:

Result	Units
Displacement	mm, cm, m
Forces, of beams and of reactions	N, kN, MN
Moments, of beams and of reactions	N·mm, N·m, kN·cm, kN·m, MN·m
Every stress	kPa (= kN/m²), MPa (= N/mm²), kN/cm²
Shell membrane forces and shears	N/m, kN/m, MN/m
Shell moments	N·m/m, kN·m/m, MN·m/m

The unit picked applies to everything Model View gives out for that result: the values written on the model, the Info and Values outputs, and the Range, which is typed in it. A Legend fed from Values therefore reads in it too. Each result keeps its own choice, so beam stresses can be in MPa while shell stresses are in kPa.

The menu changes only what Model View displays. The result components always give out the units in the tables above.

See also

• Materials — the units of E, G and Rho
• Results — reading the numbers
• Model View — the Unit menu
• Axes and signs — which way the numbers point